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Math Help - A simple probability question

  1. #1
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    A simple probability question

    The probability of happening the event A is 0.7 and that of event B is 0.5. If the events are independent, what is the probability of of happening

    a) either of them
    b) none of them


    I know its simple..but I am stuck

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  2. #2
    Super Member girdav's Avatar
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    Re: A simple probability question

    Just write the definition of independence. What is it?
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  3. #3
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    Re: A simple probability question

    Ans for qn. b). is 0.01.

    But have doubt with qn. a) ..I think it is P (A or B) . not P (A and B).
    so the ans is 1- 0.01 = .99.
    is this correct?
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  4. #4
    Super Member girdav's Avatar
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    Re: A simple probability question

    I also think that it's P(A\cup B).. But I don't understand why you find 0.01 for P(A^c\cap B^c).
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  5. #5
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    Re: A simple probability question

    a) Since the events are not mutually exclusive, P (A or B)= P(A) + P (B) - P (AUB) = 0.7+ 0.5 - 0.35=0.85

    b) 1-0.85 = 0.15

    Please discard the previous ans. instead of 0.7 i used 0.8 for P(A). Now I hope I am correct. am I?
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  6. #6
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    Re: A simple probability question

    P(A union B)=P(A)+P(B)-P(A intersection B) (see Probability of a union here)
    but A and B are independent implies P(A intersection B)=P(A)*P(B)
    As a consequence:
    P(either happens)=P(A union B)=P(A)+P(B)-P(A intersection B)=P(A)+P(B)-P(A)*P(B)=0.7+0.5-0.7*0.5=0.85
    and
    P(none happens)=1-P(either happens)=1-0.85=0.15
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  7. #7
    Super Member girdav's Avatar
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    Re: A simple probability question

    Yes, except that in the formular for P(A or B) it's P(A\cap B), not P(A\cup B).
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    Re: A simple probability question

    thanks for both of you
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